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#### Resources tagged with Angle properties of shapes similar to Exploring 2D Shapes:

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### There are 21 results

Broad Topics > 2D Geometry, Shape and Space > Angle properties of shapes

### Arclets Explained

##### Stage: 3 and 4

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

### Tricircle

##### Stage: 4 Challenge Level:

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .

##### Stage: 4 Challenge Level:

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

### Bisecting Angles in a Triangle

##### Stage: 3 and 4 Challenge Level:

Measure the two angles. What do you notice?

### Pentakite

##### Stage: 4 and 5 Challenge Level:

ABCDE is a regular pentagon of side length one unit. BC produced meets ED produced at F. Show that triangle CDF is congruent to triangle EDB. Find the length of BE.

### At a Glance

##### Stage: 4 Challenge Level:

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

### Terminology

##### Stage: 4 Challenge Level:

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

### Angles in Three Squares

##### Stage: 3 and 4 Challenge Level:

Drawing the right diagram can help you to prove a result about the angles in a line of squares.

##### Stage: 3 and 4 Challenge Level:

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

### Pent

##### Stage: 4 and 5 Challenge Level:

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

### No Right Angle Here

##### Stage: 4 Challenge Level:

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

### A Sameness Surely

##### Stage: 4 Challenge Level:

Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST and PU are perpendicular to AB produced. Show that ST + PU = AB

### Golden Triangle

##### Stage: 5 Challenge Level:

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.

##### Stage: 5 Short Challenge Level:

Can you work out where the blue-and-red brick roads end?

### Triangles and Petals

##### Stage: 4 Challenge Level:

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

##### Stage: 4 Challenge Level:

Points D, E and F are on the the sides of triangle ABC. Circumcircles are drawn to the triangles ADE, BEF and CFD respectively. What do you notice about these three circumcircles?

### LOGO Challenge 4 - Squares to Procedures

##### Stage: 3 and 4 Challenge Level:

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

### First Forward Into Logo 9: Stars

##### Stage: 3, 4 and 5 Challenge Level:

Turn through bigger angles and draw stars with Logo.

### Dodecawhat

##### Stage: 4 Challenge Level:

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

### First Forward Into Logo 7: Angles of Polygons

##### Stage: 3, 4 and 5 Challenge Level:

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

### Logo Challenge 3 - Star Square

##### Stage: 2, 3 and 4 Challenge Level:

Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles